The invention is directed to high accuracy thickness measurements and in particular to a multi-frequency electronic apparatus for remotely measuring the thickness of dielectric layers.
Conventional electronic apparatus used for the determination of the thickness of layers such as industrial films and sheets, or sea ice layers encounter significant problems arising from conflicts between desired accuracy requirements and realizable bandwidth capabilities.
Experimental electromagnetic measurements for sea ice indicate that losses are minimum over the HF and VHF spectrum. Consequently, a successful remote sensing system for sea ice should operate in these frequency bands. However, the maximum accuracy achieved for a modulated carrier apparatus operating in the VHF band, say under 200 MHz, is of the order of 1 ft. This is unsatisfactory for many important applications such as the clearing of ice blockage in shipping lanes or the determination of the thickness of ice landing-strips and roadways for Arctic exploration.
A similar problem exists in the remote production line measurements of industrial film thicknesses such as oil, and industrial sheet thicknesses such as plexiglass or building materials. The large bandwidths and high centre frequencies required by conventional electronic systems for satisfactory accuracy are prohibitive due to high cost and stringent component requirements. A reduction in centre frequency and bandwidth would alleviate this problem; however, the accuracy attainable would become unsatisfactory.
It is apparent that a reduction in centre frequency and bandwidth is required while maintaining as high an accuracy as possible.
The operation of systems such as homodyne measurement systems, interferometers, holographic systems and synthetic-aperture radars is dependent on the principle of coherency which refers to the presence of an analytic relationship between the phases of diverse wave at different points in time. This principle is discussed by M. J. Beran and G. B. Parrent in the text "Theory of Partial Coherence", Prentice-Hall, New Jersey, 1964. Generally, coherency is referred to in the form of spatial coherency, i.e. the conservation of a phase reference between several spatially distributed and differentially delayed signals of the same frequency. Two fundamental properties of this principle, the maximum phase resolution obtainable in the presence of noise and the maximum differential time delay tolerable between the signals, determine important engineering constraints for any spatial interferometric application.
The maximum phase accuracy which can be achieved between two spatially isolated signals for a typical phase measurement system in which a low power, noise embedded signal is received from a target and is compared with a high power, noise free transmitter signal, can be derived to be: ##EQU1## where
.phi..sub.0 = phase error which is exceeded only 1% of the time;
A = amplitude of the received signal;
N.sub.0 = the one-sided power spectral density of the noise; and
BW = effective bandwidth of the bandpass filter.
This equation allows a comparison of the spatial accuracies which can be obtained for a conventional modulated carrier (MC) electronic measurement system and a continuous wave (CW) phase measurement apparatus.
For a continuous wave system operating with a frequency f, the relation between phase and delay is: ##EQU2## where T is the half-power width of the continuous wave sinusoid, Eqn. (2) becomes: ##EQU3## With this, Eqn. (1) gives: ##EQU4## As a result, the required signal to noise ratio necessary to achieve a desired error in delay for a continuous wave system operating at a specified half-power width can be found.
For a conventional modulated carrier system, the broadband noise at the input of the system's front end matched filter is changed at the output into narrow band noise fluctuating at the same average frequency as the filter response. The filter response can then be represented mathematically by a pure sinusoid of the same amplitude and half-power width as the central peak of the system response. The noise will now manifest itself predominantly as a phase shift of this sinusoid and Eqn. (5) can be used to obtain a delay error. If the amplitude and half-power width of the central peak is matched to the sinusoid of the continuous wave system response, then the ratio of the errors in delay given by Eqn. (5) can be written: ##EQU5##
This relationship compares the resolution achievable for the two types of systems and is dependent only on the ratio of the bandwidths of the two front-end filters. Now, for an MC system, the bandwidth of the matched filter is approximately equal to the inverse of the half-power width of the signal pulse: EQU BW.sub.MC = 1/T (7)
for a CW system, bandpass filters with 0.04% to 4% relative bandwidths are easily constructed. Using Eqn. (3); this gives: EQU 0.0001/T &lt; BW.sub.CW &lt; 0.01/T (8)
substituting Eqn. (7) and (8), Eqn. (6) yields: ##EQU6## This equation demonstrates that one or two orders of magnitude improvement in range precision can be achieved for the CW system as compared to the MC system. Alternatively, one or two orders of magnitude reduction in centre frequency becomes possible for the CW system while maintaining the high resolution capability of the MC system.
The second fundamental property of coherency, the maximum differential time delay which can be tolerated between the separate signals without disturbing their analytical phase relationship, can be shown to be dependent on the effective bandwidth of the AM and FM noise associated with the signals. It has been determined that the maximum differential time delay is given by the autocorrelation interval of the noise: EQU R.sub.n (.tau.) .apprxeq. 1/BW (10)
where BW = bandwidth of the noise.
Since this interval is inversely related to the bandwidth of the modulating noise, a large difference in signal time delays and consequently in signal path lengths can be tolerated for noise-free oscillating sources.
The synchronous detection process which provides the time reference in a CW system can be easily implemented by a comparison of the phases of the transmitted and returned signals. This technique is commonly used to determine the distance to a single, stationary target in surveying applications. However, three limitations of this comparison technique exist in situations where the distance to the target can be large and varying as in remote sensing applications.
The first limitation arises in situations where the distance to the target is larger than one-half of the product of the speed of light and the signal autocorrelation interval, l &gt; .nu.R.sub.s (.tau.)/2. For such large distances, the transmitted and received signals will begin to lose their coherency and synchronous detection becomes impossible. This situation may arise in environmental monorating from the upper atmosphere or space.
A second and more severe limitation also arises from the large difference in path lengths between the transmitted reference signal and the received signal. The phase detection networks form high Q resonant circuits and consequently any local oscillator frequency drift will completely obscure initial phase alignments. This becomes difficult to avoid in environmental testing due to the extreme termperature differentials encountered.
The third and most severe limitation arises from motion between the instrument and the target during the finite time integration interval T used in the synchronous detection provess to improve sensitivity. Relative motion, which is impossible to avoid during continuous profiling experiments, will completely disrupt the analyticity of the detected phases.